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SHARP CONSTANTS IN THE POINCARÉ, STEKLOV AND RELATED INEQUALITIES (A SURVEY)

Part of: Partial differential equations Linear function spaces and their duals Inequalities

Published online by Cambridge University Press:  10 October 2014

Nikolay Kuznetsov  and
Alexander Nazarov
Nikolay Kuznetsov
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Science, St. Petersburg, Russia email nikolay.g.kuznetsov@gmail.com
Alexander Nazarov
Affiliation:
Laboratory of Mathematical Physics, St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia Department of Mathematical Physics, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia email al.il.nazarov@gmail.com
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Abstract

During the past 55 years substantial progress concerning sharp constants in Poincaré-type and Steklov-type inequalities has been achieved. Original results of H. Poincaré, V. A. Steklov and his disciples are reviewed along with the main further developments in this area.

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals

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Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015 , pp. 328 - 344
Copyright
Copyright © University College London 2014 

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